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Q6.1: SYSTEMS OF PARTICLES AND ROTATIONAL MOTION Solutions — NCERT Physics - Part 1
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently assume the centre of mass must lie within the material of the object; this fails for hollow or ring‑shaped bodies where symmetry places the COM at the geometric centre, which can be empty space. Always determine the COM from symmetry or integration, not from the intuition that it must be inside the body.
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?
Step-by-Step Verified Solution
**Answer:** (i) Sphere: geometric centre. (ii) Cylinder: midpoint of its axis. (iii) Ring: geometric centre (outside the material). (iv) Cube: geometric centre. No, the centre of mass need not lie inside the body (e.g., a ring).
**Step-by-Step Explanation:**
For uniform symmetric bodies, the centre of mass lies at the geometric centre. For a ring, the centre of mass is at its centre, which is outside the material of the ring [citation:33].
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